Energy-based comparison of various controllers for vibration suppression using piezoceramics

Abstract

The large-scale and light-weight design trend in aircraft and spacecraft results in extremely flexible structures with lowfrequency vibration modes. Suppression of undesired vibrations in such flexible structures with limited energy is becoming an important design problem to develop energy-autonomous controllers powered using the harvested ambient energy. The objective of this paper is to compare different control laws to suppress low-frequency vibrations using the minimum actuation energy for the same system and under the same design constraint (identical settling time for free vibrations). The vibration suppression performance of four active control systems as well as their hybrid versions employing a switching technique are presented and compared. The control systems compared here are a Positive Position Feedback (PPF) controller, a Proportional Integral Derivative (PID) controller, a nonlinear controller (with a second-order nonlinear term multiplying the position and velocity feedback to create variable damping), a Linear Quadratic Regulator (LQR) controller and their hybrid versions integrating a bang-bang control law (on-off control) with each of these controllers. Experimental results are presented for a thin cantilevered beam with a piezoceramic transducer controlled by these eight controllers with a focus on the fundamental vibration mode under transverse free vibrations and the control energy requirements are compared. Experiments results reveal that all the controllers reduce the vibration settling time to 0.85s as a design constraint (which is 92.3% of the open-loop settling time: 10.9s). The average actuation power input provided to the piezoceramic transducer in each case is obtained for the time current and voltage measurements until the settling time. Comparisons show that the switching technology reduces significant actuation power requirement, so that all the hybrid control systems require much less power than their conventional versions. Especially, the hybrid bang-bang-nonlinear controller requires 67% less power than the conventional nonlinear controller. In order to verify this statement, the actuation current is theoretically calculated through piezo-capacitance using voltage measurements to check out the average power estimation. The theoretical checking out provides the same results with slightly error, which can be explained by measurement errors.